Prepare and bake the cake according to the package directions in a 9-by-13-inch pan at 350°F (175°C), usually for 25 to 30 minutes. Let the cake cool completely, which takes about 1 hour.

Trim away any very dry or browned edges, then crumble the cooled cake into fine crumbs in a large bowl. Add 1/3 cup frosting and mix thoroughly, adding more only if needed until the mixture holds together when pressed without becoming wet or sticky.

Portion the mixture into roughly 1-tablespoon pieces and roll each portion between your palms into a smooth ball. Arrange the balls on a parchment-lined tray and chill them for 1 to 2 hours, or until firm.

Melt the candy coating according to the package directions. If it seems too thick for dipping, stir in a small amount of the optional shortening or paramount crystals rather than adding water.

Dip the end of each stick into a little melted coating, then insert it about halfway into a chilled cake ball. Allow the coating to set briefly so it acts as a glue that helps keep the cake pop attached.

Dip each cake pop straight down into the melted coating, lift it out, and gently tap the stick while rotating it to remove excess coating. Add sprinkles or other decorations immediately, before the shell sets.

Place each finished cake pop upright in a cake-pop stand or a block of Styrofoam until firm. Serve once the coating has set, or keep the pops covered until your celebration.